1. Field of the Invention
The invention relates to a method for obtaining a temperature-independent voltage reference by means of an energy gap reference circuit using at least one bipolar transistor and a voltage source as well as a circuit arrangement for obtaining a temperature-independent voltage reference.
2. Prior Art
When using bipolar transistors as well as electronic components such as, for instance, analog-to-digital converters (A/D converters), known temperature dependences of the transistor parameters, or of the circuit, will have to be taken into account if a temperature-independent voltage reference is to be provided. In particular, the characteristic data of a bipolar transistor are strongly temperature-dependent, the temperature-dependent context between the collector current IC and the base emitter voltage UBE being of particular relevance. The dependence of UBE on the temperature T results from the following equation:                               I          C                =                              I            S                    ⁢          e          ⁢                                    qU              BE                        kT                                              (        1        )            
The reason for such a temperature dependence of IC is the temperature dependence of the cutoff current IS and of the temperature voltage             U      T        =          kT      q        ,
wherein, taking into account the temperature dependence of the cutoff current                                           I            S                    =                      Ae            ⁢                                          -                                  qU                  G                                            kT                        ⁢                          T              X                                      ,                  
                ⁢                  the following relation applies:                                    (        2        )                                                      I            C                    =                      Ae            -                                                            U                  G                                ⁢                q                            kT                        +                                                                                U                    BE                                    ⁢                  q                                kT                            ⁢                              T                X                                                    ,                            (        3        )            
in which k is the Boltzmann constant (1.38xc3x9710xe2x88x9223 VAs/K), q is the elementary charge=1.602xc3x9710xe2x88x9219 As, UG≈1.12 V is the (band) gap voltage of silicon, T is the temperature, x is an empirical constant and A is a proportionality factor. In known circuit arrangements, the temperature dependence of UG is usually neglected.
With most bipolar transistors, an increase of Ic to double its value results from the above relations at a temperature increase by 11xc2x0 K. In circuits that serve to obtain voltage references, it has already been known to basically use as a voltage reference the base emitter voltage of a bipolar transistor. In such known analog circuits, a voltage having a symmetrically equal positive temperature coefficient is added in order to compensate for the known high temperature dependence, said voltage being generated in a second transistor. Therefore, the known gap voltage reference circuits used to obtain a voltage reference, as a rule, presuppose two transistors selected as to their characteristics, the selection having to be made with slight tolerances.
The invention aims to provide a method of the initially defined kind, which uses only a single bipolar transistor and, therefore, renders the selection of a second transistor tuned to the characteristics of the first transistor superfluous. Moreover, the invention aims to further reduce the temperature dependence of the measured values and to achieve a temperature compensation at a substantially higher accuracy. To solve this object, the method according to the invention essentially consists in that only a single bipolar transistor is connected in series with a resistor, that different voltages are facultatively applied, that the voltages are detected upstream and downstream of the series resistor and fed to an A/D converter and that the gain constant of the A/D converter is calculated from the digitalized measurements and used to correct the measurements. The fact that, within the context of the method according to the invention, an A/D converter is used in addition and the signals are subsequently processed in the digital form, additionally involves the temperature dependence of such ADC circuits, which must be compensated for. Within the context of the method according to the invention, the gain constant of the A/D converter, therefore, is determined from a plurality of measurenments for the respectively prevailing temperature and may each be updated accordingly such that actually corrected values will be available, which are characterized by a higher precision than is feasible with analog circuits.
According to a preferred realization of the method according to the invention, it is proceeded in a manner that, in order to correct the ADC gain constant, a value for the base emitter voltage of the bipolar transistor and a value for the cutoff current of the bipolar transistor are measured from the voltage drop on the resistor and that, by applying a computational technique, the temperature-dependent portions of the two measured values are eliminated and a gain constant applying for the respective temperature prevailing at the time of measurement is determined.
In order to determine the gain constant, it is proceeded within the context of the method according to the invention in a manner that the gain constant is calculated by                     S        =                                            -              1                        -                          ln              ⁢                              xe2x80x83                            ⁢                              I                x                                      +            x            +                          ln              ⁢                              xe2x80x83                            ⁢              A                        +                          x              ⁢                              xe2x80x83                            ⁢              ln              ⁢                              q                                  d                  ⁢                                      xe2x80x83                                    ⁢                  ln                  ⁢                                      xe2x80x83                                    ⁢                                      I                    x                                    ⁢                  k                                                      +                          ln              ⁢                              xe2x80x83                            ⁢              R                                                          -              1                        +                          d              ⁢                              xe2x80x83                            ⁢              ln              ⁢                              xe2x80x83                            ⁢                              I                x                            ⁢                              U                G                                      +            x                                              (        13        )            
wherein lnIx is the natural logarithm of the measurement for the collector current, x and A are constants, R is the resistance and UG is the (band) gap voltage (for Si≈1.12 V). Since the gain constant always is each newly calculated from a plurality of measurements by the algorithm explained in more detail below, it is feasible within the context of the method according to the invention and in correspondence with a preferred further development that the value for S is updated continuously or at regular time intervals and applied to calculate the actual reference voltage and, if desired, to precisely determine test voltages.
The circuit arrangement according to the invention used to obtain a temperature-independent reference voltage may be designed in a particularly simple manner, requiring but a small number of components. The circuit arrangement is essentially characterized in that it comprises, placed in series, a bipolar transistor and a resistor R connected with the transistor, that an A/D converter (ADC) configured to yield digitalized voltage measurements is connected via switches to ports provided on either side of the resistor R, and that the digital ADC signals are fed to a computer to determine the gain constant, from which the corrected voltage signal can be read out digitally.
The switch in a particularly simple manner may be designed as a multiplexer component whose inputs are switched by a control signal of the computer and comprise connectors or ports at which the voltages to be measured are applied by actuation of the associated switch. The multiplexer, thus, transmits the analog signals to the analog input of the ADC as a function of the switch position. In principle, the circuit arrangement may be established using PNP or NPN transistors. In the case of PNP transistors, the emitter is connected with the resistor and the collector that is coupled with the base is connected to ground, the adjustable voltage source being connected to the other port of the resistor.
A preferred use of the circuit arrangement according to the invention is the use in a digital voltmeter, the principal mode of operation as well as the circuit arrangement being in no way limited to such digital voltmeters.
In the following, the invention will be explained in more detail by way of the computational algorithm chosen for the calculation of the gain constant and by way of an exemplary circuit used with a digital voltmeter.
Departing from the basic relationship reflecting the dependence of UBE on the temperature T in a bipolar transistor                                           I            C                    =                                    I              S                        ⁢            e            ⁢                                          qU                BE                            kT                                      ,                            (        1        )            
it is then further considered that not only the collector current but also the cutoff current IS is temperature-dependent. The temperature dependence of the cutoff current follows the relation                                           I            S                    =                      Ae            ⁢                                          -                                  qU                  G                                            kT                        ⁢                          T              x                                      ,                            (        2        )            
the meanings indicated above also applying in the instant relations.
By inserting the meaning IS according to equation (2) in the equation (1), the relation                               I          C                =                              Ae            ⁢                          xe2x80x83                        ⁢                                                            -                                      U                    G                                                  ⁢                q                            kT                                +                                                                      U                  BE                                ⁢                q                            kT                        ⁢                          T              x                                                          (        3        )            
will be obtained.
When using an A/D converter, a temperature-dependent gain S is imparted on the analog measurements in the ADC, which would cause respective errors if no temperature compensation were effected. For the computational elimination of such errors, UBE is at first replaced with Ux, from which results the relation       U    BE    =            U      x        S  
with Ux indicating the measured voltage that is to be corrected by applying the correct gain constant. In the same manner, Ic may be replaced with the actual value Ix, which is measured as a voltage drop on the resistor R and must have the same gain constant S. Appropriate substitution yields the relation                                           I            C                    =                                    e              ⁢                              xe2x80x83                            ⁢              ln              ⁢                              xe2x80x83                            ⁢                              I                x                                      RS                          ,                            (        4        )            
whereby the natural logarithm of this current measurment is subsequently expressed according to the relation                               ln          ⁢                      xe2x80x83                    ⁢                      I            x                          =                              ln            ⁡                          [                                                Ae                  ⁢                                      xe2x80x83                                    ⁢                                                                                    -                                                  U                          G                                                                    ⁢                      q                                        kT                                                  +                                                                                                    U                        x                                            ⁢                      q                                        kT                                    ⁢                                      RST                    x                                                              ]                                .                                    (        5        )            
By this relation, the graphic representation of the dependence of Ix and Ux, thus, becomes feasible, lnIx being plotted on the Y-axis and Ux being plotted on the X-axis. There will be obtained a straight line with the slope dlnIx, which intersects the Y-axis in point Ux=0 at the respective value of dlnIx. Thus, the slope of this straight line is                               d          ⁢                      xe2x80x83                    ⁢          ln          ⁢                      xe2x80x83                    ⁢                      I            x                          =                              q            kST                    .                      
                    ⁢                      By solving this relation for T,                                              (        6        )                                T        =                  q                      d            ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          I              x                        ⁢            kS                                              (        7        )            
is obtained.
At the point Ux=0, upon insertion in                                           ln            ⁢                          xe2x80x83                        ⁢                          I              x                                =                      ln            ⁢                          xe2x80x83                        [                                          Ae                ⁢                                  xe2x80x83                                ⁢                                                                            -                                              U                        G                                                              ⁢                    q                                    kT                                            +                                                                                          U                      x                                        ⁢                    q                                    kT                                ⁢                                  RST                  x                                                      ]                          ,                  
                ⁢                  the relation                                    (        5        )                                          ln          ⁢                      xe2x80x83                    ⁢                      I            x                          =                  ln          ⁢                      xe2x80x83                    [                      Ae            ⁢                                                            -                                      U                    G                                                  ⁢                q                            kT                        ⁢                          RST              x                                ]                                    (        8        )            
may then be derived. By the appropriate transformation of this equation, the relations                                           ln            ⁢                          xe2x80x83                        ⁢                          I              x                                =                                                                      -                                      U                    G                                                  ⁢                q                            kT                        +                          ln              ⁢                              xe2x80x83                            ⁢              A                        +                          ln              ⁢                              xe2x80x83                            ⁢              R                        +                          ln              ⁢                              xe2x80x83                            ⁢              S                        +                          x              ⁢                              xe2x80x83                            ⁢              ln              ⁢                              xe2x80x83                            ⁢              T                                      ⁢                  
                ⁢                  and          ,                      xe2x80x83                    ⁢          furthermore          ,                                    (        9        )                                                      ln            ⁢                          xe2x80x83                        ⁢                          I              x                                =                                                    -                d                            ⁢                              xe2x80x83                            ⁢              ln              ⁢                              xe2x80x83                            ⁢                              I                x                            ⁢                              U                G                            ⁢              S                        +                          ln              ⁢                              xe2x80x83                            ⁢              A                        +                          ln              ⁢                              xe2x80x83                            ⁢              R                        +                          x              ⁢                              xe2x80x83                            ⁢              ln              ⁢                              xe2x80x83                            ⁢                              q                                  d                  ⁢                                      xe2x80x83                                    ⁢                  ln                  ⁢                                      xe2x80x83                                    ⁢                                      I                    x                                    ⁢                  ks                                                      +                          ln              ⁢                              xe2x80x83                            ⁢              S                                      ⁢                  
                ⁢                  and          ,                      xe2x80x83                    ⁢          finally          ,                                    (        10        )                                          ln          ⁢                      xe2x80x83                    ⁢                      I            x                          =                                            -              d                        ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          I              x                        ⁢                          U              G                        ⁢                          xe2x80x83                        ⁢            S                    +                      ln            ⁢                          xe2x80x83                        ⁢            A                    +                      x            ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          q                              d                ⁢                                  xe2x80x83                                ⁢                ln                ⁢                                  xe2x80x83                                ⁢                                  I                  x                                ⁢                k                                              +                      ln            ⁢                          xe2x80x83                        ⁢            R                    +                      ln            ⁢                          xe2x80x83                        ⁢            S                    -                      x            ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          S              .                                                          (        11        )            
are obtained.
From this relation, it is clearly apparent that the absolute temperature T does no longer appear in the determination of the true value of the gain constant S, said relation merely containing universal constants UG, q, k as well as the known values as well as temperature-independent expressions x, A and the value R which is only slightly temperature-dependent. If, in addition, the temperature dependence of R is to be taken into account, this may, for instance, be effected by a suitable modification of the value X.
In order to solve this equation, a Taylor expansion of the first order may be effected for in S by the value 1.0, from which results                               ln          ⁢                      xe2x80x83                    ⁢                      I            x                          =                              -            1                    +          S          +                      d            ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          I              x                        ⁢                          U              G                        ⁢            S                    -                                    (                                                -                  1                                +                S                            )                        ⁢            x                    +                      ln            ⁢                          xe2x80x83                        ⁢            A                    +                      x            ⁢                          xe2x80x83                        ⁢            ln            ⁢                          xe2x80x83                        ⁢                          q                              d                ⁢                                  xe2x80x83                                ⁢                ln                ⁢                                  xe2x80x83                                ⁢                                  I                  x                                ⁢                k                                              +                      ln            ⁢                          xe2x80x83                        ⁢                          R              .                              
                            ⁢              From                        ⁢                          xe2x80x83                        ⁢            the            ⁢                          xe2x80x83                        ⁢            solution            ⁢                          xe2x80x83                        ⁢            of            ⁢                          xe2x80x83                        ⁢            this            ⁢                          xe2x80x83                        ⁢            equation            ⁢                          xe2x80x83                        ⁢            follows                                              (        12        )                                s        =                                                            -                1                            -                              ln                ⁢                                  xe2x80x83                                ⁢                                  I                  x                                            +              x              +                              ln                ⁢                                  xe2x80x83                                ⁢                A                            +                              x                ⁢                                  xe2x80x83                                ⁢                ln                ⁢                                  q                                      d                    ⁢                                          xe2x80x83                                        ⁢                    ln                    ⁢                                          xe2x80x83                                        ⁢                                          I                      x                                        ⁢                    k                                                              +                              ln                ⁢                                  xe2x80x83                                ⁢                R                                                                    -                1                            +                              d                ⁢                                  xe2x80x83                                ⁢                ln                ⁢                                  xe2x80x83                                ⁢                                  I                  x                                ⁢                                  U                  G                                            +              x                                .                                    (        13        )            
Overall, x, A and R may be calibrated individually for every circuit arrangement, particularly suitable values being precalculatable by simulation.
In a continuous self-calibrating system, the value for the gain constant S may each be updated continuously or at regular time intervals such that precise values will always be obtained iteratively. On grounds of such an iteration procedure, it is also readily permissible to insert only one Taylor expansion of the first order in the above calculation.
Without any particular calibration, an accuracy of about 1% may be reached by such calculations. If the values for x, A and R are suitably optimized, the accuracy may even be enhanced to below 0.1% at an operating temperature range of about 100xc2x0 K.